Unlike mathematics, it loses meaning when explained; it is the last line of Beckett's idiosyncratic novel Watt. Seemed an appropriate response to your enigmatic comment...
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copper.hatJun 24 '12 at 23:47

What I mean is that if one chooses an appropriate "fancy" partition the solution is much manageable (i.e. qoqozs solution or Amihai's), which I guess you're refering to.
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Pedro Tamaroff♦Jun 25 '12 at 0:09

Now, we need to calculate the upper and lower Darboux sums in respect to the $P_n$'s. Notice that $\frac{1}{x}$ is monotonic decreasing on the interval so the $\sup$ and the $\inf$ are obtained on the edges:

Well, how do you define $\ln b$? This seems circular. THe derivative of $b^x$ is defined using that of $e^x$, which might or might not be defined in terms of the $\log x$.
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Pedro Tamaroff♦Jun 22 '12 at 16:05

Why can't I define the logarithm as the inverse of the $\exp$?
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Amihai ZivanJun 23 '12 at 17:36

I said "might or might not" in the sense you can choose that method, but there are others available.
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Pedro Tamaroff♦Jun 24 '12 at 0:06